TSTP Solution File: SWW535_5 by Leo-III---1.7.15

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SWW535_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Jun 24 18:23:36 EDT 2024

% Result   : Theorem 120.71s 43.04s
% Output   : Refutation 121.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   83
%            Number of leaves      :  133
% Syntax   : Number of formulae    :  686 ( 156 unt;   0 typ;   0 def)
%            Number of atoms       : 5734 ( 715 equ;   0 cnn)
%            Maximal formula atoms :   41 (   8 avg)
%            Number of connectives : 17080 ( 559   ~; 360   |;  47   &;15908   @)
%                                         (  20 <=>; 186  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   83 (  14 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   51 (  48 usr;  10 con; 0-5 aty)
%            Number of variables   : 5246 (   0   ^5241   !;   5   ?;5246   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(bool_type,type,
    bool: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(bounded_lattice_type,type,
    bounded_lattice: 
      !>[TA: $tType] : $o ).

thf(one_type,type,
    one: 
      !>[TA: $tType] : $o ).

thf(zero_type,type,
    zero: 
      !>[TA: $tType] : $o ).

thf(bot_type,type,
    bot: 
      !>[TA: $tType] : $o ).

thf(lattice_type,type,
    lattice: 
      !>[TA: $tType] : $o ).

thf(semiring_1_type,type,
    semiring_1: 
      !>[TA: $tType] : $o ).

thf(semiring_char_0_type,type,
    semiring_char_0: 
      !>[TA: $tType] : $o ).

thf(comm_semiring_1_type,type,
    comm_semiring_1: 
      !>[TA: $tType] : $o ).

thf(comm_monoid_add_type,type,
    comm_monoid_add: 
      !>[TA: $tType] : $o ).

thf(ab_semigroup_add_type,type,
    ab_semigroup_add: 
      !>[TA: $tType] : $o ).

thf(semilattice_inf_type,type,
    semilattice_inf: 
      !>[TA: $tType] : $o ).

thf(cancel_semigroup_add_type,type,
    cancel_semigroup_add: 
      !>[TA: $tType] : $o ).

thf(bounded_lattice_bot_type,type,
    bounded_lattice_bot: 
      !>[TA: $tType] : $o ).

thf(cancel146912293up_add_type,type,
    cancel146912293up_add: 
      !>[TA: $tType] : $o ).

thf(linord219039673up_add_type,type,
    linord219039673up_add: 
      !>[TA: $tType] : $o ).

thf(semiri456707255roduct_type,type,
    semiri456707255roduct: 
      !>[TA: $tType] : $o ).

thf(combb_type,type,
    combb: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).

thf(combc_type,type,
    combc: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).

thf(combk_type,type,
    combk: 
      !>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).

thf(combs_type,type,
    combs: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).

thf(one_one_type,type,
    one_one: 
      !>[TA: $tType] : TA ).

thf(plus_plus_type,type,
    plus_plus: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(zero_zero_type,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

thf(huffma675207370phabet_type,type,
    huffma675207370phabet: 
      !>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > ( fun @ TA @ bool ) ) ).

thf(huffma1518433673istent_type,type,
    huffma1518433673istent: 
      !>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > $o ) ).

thf(huffma1134658180e_cost_type,type,
    huffma1134658180e_cost: 
      !>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).

thf(huffma410068972_depth_type,type,
    huffma410068972_depth: 
      !>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > TA > nat ) ).

thf(huffma1352802255e_freq_type,type,
    huffma1352802255e_freq: 
      !>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > TA > nat ) ).

thf(huffma1146269203erNode_type,type,
    huffma1146269203erNode: 
      !>[TA: $tType] : ( nat > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) ) ).

thf(huffma2021818691e_Leaf_type,type,
    huffma2021818691e_Leaf: 
      !>[TA: $tType] : ( nat > TA > ( huffma1450048681e_tree @ TA ) ) ).

thf(huffma107959123e_case_type,type,
    huffma107959123e_case: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ TA ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).

thf(huffma1280178957ee_rec_type,type,
    huffma1280178957ee_rec: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).

thf(huffma83463279weight_type,type,
    huffma83463279weight: 
      !>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).

thf(inf_inf_type,type,
    inf_inf: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(semiring_1_of_nat_type,type,
    semiring_1_of_nat: 
      !>[TA: $tType] : ( nat > TA ) ).

thf(bot_bot_type,type,
    bot_bot: 
      !>[TA: $tType] : TA ).

thf(collect_type,type,
    collect: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).

thf(aa_type,type,
    aa: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fconj_type,type,
    fconj: fun @ bool @ ( fun @ bool @ bool ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).

thf(pp_type,type,
    pp: bool > $o ).

thf(t_1_type,type,
    t_1: huffma1450048681e_tree @ a ).

thf(t_2_type,type,
    t_2: huffma1450048681e_tree @ a ).

thf(w_type,type,
    w: nat ).

thf(8,axiom,
    ! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
        = ( huffma2021818691e_Leaf @ TA @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_tree_Osimps_I1_J) ).

thf(150,plain,
    ! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
      ( ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
          = ( huffma2021818691e_Leaf @ TA @ B @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( huffma2021818691e_Leaf @ TA @ D @ C )
          = ( huffma2021818691e_Leaf @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(153,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( C = A ) ),
    inference(cnf,[status(esa)],[150]) ).

thf(157,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( C = A ) ),
    inference(lifteq,[status(thm)],[153]) ).

thf(1,conjecture,
    ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) )
    = ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) )
   != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(135,plain,
    ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) )
   != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(136,plain,
    ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) )
   != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ),
    inference(lifteq,[status(thm)],[135]) ).

thf(1084,plain,
    ! [D: nat,C: huffma1450048681e_tree @ a,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ A ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C != t_2 ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1085,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_2 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ A ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1084:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 ))]]) ).

thf(1168,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_2 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ A ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1085]) ).

thf(71,axiom,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
          = ( bot_bot @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_inf__bot__left) ).

thf(347,plain,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
          = ( bot_bot @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(152,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( D = B ) ),
    inference(cnf,[status(esa)],[150]) ).

thf(156,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( D = B ) ),
    inference(lifteq,[status(thm)],[152]) ).

thf(627,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ B ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( D
       != ( huffma1134658180e_cost @ a @ t_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(628,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ t_1 ) @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ B ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[627:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( huffma1134658180e_cost @ a @ t_1 ))]]) ).

thf(103,axiom,
    lattice @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).

thf(445,plain,
    lattice @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(6,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TA )
     => ( lattice @ ( fun @ TB @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).

thf(145,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TA )
     => ( lattice @ ( fun @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(146,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ ( lattice @ TB )
      | ( lattice @ ( fun @ TA @ TB ) ) ),
    inference(cnf,[status(esa)],[145]) ).

thf(560,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ ( fun @ TA @ TB ) )
      | ( ( lattice @ nat )
       != ( lattice @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[445,146]) ).

thf(561,plain,
    ! [TA: $tType] : ( lattice @ ( fun @ TA @ nat ) ),
    inference(pattern_uni,[status(thm)],[560:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( nat ))]]) ).

thf(566,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( lattice @ ( fun @ TB @ TC ) )
      | ( ( lattice @ ( fun @ TA @ nat ) )
       != ( lattice @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[561,146]) ).

thf(567,plain,
    ! [TA: $tType,TB: $tType] : ( lattice @ ( fun @ TB @ ( fun @ TA @ nat ) ) ),
    inference(pattern_uni,[status(thm)],[566:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( fun @ TA @ nat ))]]) ).

thf(570,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( lattice @ ( fun @ TC @ TD ) )
      | ( ( lattice @ ( fun @ TB @ ( fun @ TA @ nat ) ) )
       != ( lattice @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[567,146]) ).

thf(571,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( lattice @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ),
    inference(pattern_uni,[status(thm)],[570:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( fun @ TB @ ( fun @ TA @ nat ) ))]]) ).

thf(581,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( lattice @ ( fun @ TD @ TE ) )
      | ( ( lattice @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) )
       != ( lattice @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[571,146]) ).

thf(582,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( lattice @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[581:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ))]]) ).

thf(585,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( lattice @ ( fun @ TE @ TF ) )
      | ( ( lattice @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) )
       != ( lattice @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[582,146]) ).

thf(586,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( lattice @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[585:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ))]]) ).

thf(596,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( lattice @ ( fun @ TF @ TG ) )
      | ( ( lattice @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) )
       != ( lattice @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[586,146]) ).

thf(597,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( lattice @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[596:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ))]]) ).

thf(600,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( lattice @ ( fun @ TG @ TH ) )
      | ( ( lattice @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) )
       != ( lattice @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[597,146]) ).

thf(601,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( lattice @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[600:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ))]]) ).

thf(607,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( lattice @ ( fun @ TH @ TI ) )
      | ( ( lattice @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) )
       != ( lattice @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[601,146]) ).

thf(608,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( lattice @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[607:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ))]]) ).

thf(666,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( lattice @ ( fun @ TI @ TJ ) )
      | ( ( lattice @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) )
       != ( lattice @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[608,146]) ).

thf(667,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( lattice @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[666:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ))]]) ).

thf(670,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( lattice @ ( fun @ TJ @ TK ) )
      | ( ( lattice @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[667,146]) ).

thf(671,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( lattice @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[670:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ))]]) ).

thf(674,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( lattice @ ( fun @ TK @ TL ) )
      | ( ( lattice @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[671,146]) ).

thf(675,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( lattice @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[674:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1352,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( lattice @ ( fun @ TL @ TM ) )
      | ( ( lattice @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[675,146]) ).

thf(1353,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( lattice @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1352:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1368,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( lattice @ ( fun @ TM @ TN ) )
      | ( ( lattice @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[1353,146]) ).

thf(1369,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( lattice @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1368:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1713,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( lattice @ ( fun @ TN @ TO ) )
      | ( ( lattice @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[1369,146]) ).

thf(1714,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( lattice @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1713:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1729,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( lattice @ ( fun @ TO @ TP ) )
      | ( ( lattice @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TP ) ) ),
    inference(paramod_ordered,[status(thm)],[1714,146]) ).

thf(1730,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( lattice @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1729:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1776,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( lattice @ ( fun @ TP @ TQ ) )
      | ( ( lattice @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TQ ) ) ),
    inference(paramod_ordered,[status(thm)],[1730,146]) ).

thf(1777,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( lattice @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1776:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2157,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( lattice @ ( fun @ TQ @ TR ) )
      | ( ( lattice @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TR ) ) ),
    inference(paramod_ordered,[status(thm)],[1777,146]) ).

thf(2158,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( lattice @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2157:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2173,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( lattice @ ( fun @ TR @ TS ) )
      | ( ( lattice @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TS ) ) ),
    inference(paramod_ordered,[status(thm)],[2158,146]) ).

thf(2174,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( lattice @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2173:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2287,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( lattice @ ( fun @ TS @ TT ) )
      | ( ( lattice @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TT ) ) ),
    inference(paramod_ordered,[status(thm)],[2174,146]) ).

thf(2288,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( lattice @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2287:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2303,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( lattice @ ( fun @ TT @ TU ) )
      | ( ( lattice @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TU ) ) ),
    inference(paramod_ordered,[status(thm)],[2288,146]) ).

thf(2304,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( lattice @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2303:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2350,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( lattice @ ( fun @ TU @ TV ) )
      | ( ( lattice @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TV ) ) ),
    inference(paramod_ordered,[status(thm)],[2304,146]) ).

thf(2351,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( lattice @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2350:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2871,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( lattice @ ( fun @ TV @ TW ) )
      | ( ( lattice @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TW ) ) ),
    inference(paramod_ordered,[status(thm)],[2351,146]) ).

thf(2872,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( lattice @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2871:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2893,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( lattice @ ( fun @ TW @ TX ) )
      | ( ( lattice @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TX ) ) ),
    inference(paramod_ordered,[status(thm)],[2872,146]) ).

thf(2894,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( lattice @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2893:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3374,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( lattice @ ( fun @ TX @ TY ) )
      | ( ( lattice @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TY ) ) ),
    inference(paramod_ordered,[status(thm)],[2894,146]) ).

thf(3375,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( lattice @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3374:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3396,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( lattice @ ( fun @ TY @ TZ ) )
      | ( ( lattice @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZ ) ) ),
    inference(paramod_ordered,[status(thm)],[3375,146]) ).

thf(3397,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( lattice @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3396:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3494,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( lattice @ ( fun @ TZ @ TZA ) )
      | ( ( lattice @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZA ) ) ),
    inference(paramod_ordered,[status(thm)],[3397,146]) ).

thf(3495,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( lattice @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3494:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3862,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( lattice @ ( fun @ TZA @ TZB ) )
      | ( ( lattice @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZB ) ) ),
    inference(paramod_ordered,[status(thm)],[3495,146]) ).

thf(3863,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( lattice @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3862:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(112,axiom,
    bot @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).

thf(481,plain,
    bot @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(79,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

thf(365,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
          = ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(3970,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( lattice @ ( fun @ TZB @ TZC ) )
      | ( ( lattice @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZC ) ) ),
    inference(paramod_ordered,[status(thm)],[3863,146]) ).

thf(3971,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( lattice @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3970:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(4414,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
      ( ( lattice @ ( fun @ TZC @ TZD ) )
      | ( ( lattice @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZD ) ) ),
    inference(paramod_ordered,[status(thm)],[3971,146]) ).

thf(4415,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( lattice @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4414:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(4982,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
      ( ( lattice @ ( fun @ TZD @ TZE ) )
      | ( ( lattice @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZE ) ) ),
    inference(paramod_ordered,[status(thm)],[4415,146]) ).

thf(4983,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( lattice @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4982:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(5470,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
      ( ( lattice @ ( fun @ TZE @ TZF ) )
      | ( ( lattice @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZF ) ) ),
    inference(paramod_ordered,[status(thm)],[4983,146]) ).

thf(5471,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( lattice @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5470:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(5926,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
      ( ( lattice @ ( fun @ TZF @ TZG ) )
      | ( ( lattice @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZG ) ) ),
    inference(paramod_ordered,[status(thm)],[5471,146]) ).

thf(5927,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( lattice @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5926:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(6052,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
      ( ( lattice @ ( fun @ TZG @ TZH ) )
      | ( ( lattice @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZH ) ) ),
    inference(paramod_ordered,[status(thm)],[5927,146]) ).

thf(6053,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( lattice @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6052:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(6424,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
      ( ( lattice @ ( fun @ TZH @ TZI ) )
      | ( ( lattice @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZI ) ) ),
    inference(paramod_ordered,[status(thm)],[6053,146]) ).

thf(6425,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( lattice @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6424:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(6911,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
      ( ( lattice @ ( fun @ TZI @ TZJ ) )
      | ( ( lattice @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZJ ) ) ),
    inference(paramod_ordered,[status(thm)],[6425,146]) ).

thf(6912,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( lattice @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6911:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(7478,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
      ( ( lattice @ ( fun @ TZJ @ TZK ) )
      | ( ( lattice @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZK ) ) ),
    inference(paramod_ordered,[status(thm)],[6912,146]) ).

thf(7479,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( lattice @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[7478:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(8012,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
      ( ( lattice @ ( fun @ TZK @ TZL ) )
      | ( ( lattice @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZL ) ) ),
    inference(paramod_ordered,[status(thm)],[7479,146]) ).

thf(8013,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( lattice @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8012:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(8146,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] :
      ( ( lattice @ ( fun @ TZL @ TZM ) )
      | ( ( lattice @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZM ) ) ),
    inference(paramod_ordered,[status(thm)],[8013,146]) ).

thf(8147,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] : ( lattice @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8146:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(8634,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] :
      ( ( lattice @ ( fun @ TZM @ TZN ) )
      | ( ( lattice @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZN ) ) ),
    inference(paramod_ordered,[status(thm)],[8147,146]) ).

thf(8635,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] : ( lattice @ ( fun @ TZM @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8634:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( TZM )),bind_type(TZN,$thf( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(9272,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType,TZO: $tType] :
      ( ( lattice @ ( fun @ TZN @ TZO ) )
      | ( ( lattice @ ( fun @ TZM @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZO ) ) ),
    inference(paramod_ordered,[status(thm)],[8635,146]) ).

thf(9273,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] : ( lattice @ ( fun @ TZN @ ( fun @ TZM @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[9272:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( TZM )),bind_type(TZN,$thf( TZN )),bind_type(TZO,$thf( fun @ TZM @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(46,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).

thf(266,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(267,plain,
    ~ ( pp @ fFalse ),
    inference(polarity_switch,[status(thm)],[266]) ).

thf(998,plain,
    ! [D: nat,C: $o,B: nat,A: $o] :
      ( ( ( huffma2021818691e_Leaf @ $o @ D @ C )
       != ( huffma2021818691e_Leaf @ $o @ B @ A ) )
      | ~ A
      | ( C
       != ( pp @ fFalse ) ) ),
    inference(paramod_ordered,[status(thm)],[157,267]) ).

thf(999,plain,
    ! [C: nat,B: nat,A: $o] :
      ( ( ( huffma2021818691e_Leaf @ $o @ C @ ( pp @ fFalse ) )
       != ( huffma2021818691e_Leaf @ $o @ B @ A ) )
      | ~ A ),
    inference(pattern_uni,[status(thm)],[998:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( pp @ fFalse )),bind(D,$thf( D ))]]) ).

thf(1327,plain,
    ! [C: nat,B: nat,A: $o] :
      ( ( ( huffma2021818691e_Leaf @ $o @ C @ ( pp @ fFalse ) )
       != ( huffma2021818691e_Leaf @ $o @ B @ A ) )
      | ~ A ),
    inference(simp,[status(thm)],[999]) ).

thf(1372,plain,
    ! [C: nat,B: nat,A: $o] :
      ( ( ( huffma2021818691e_Leaf @ $o @ C @ $false )
       != ( huffma2021818691e_Leaf @ $o @ B @ A ) )
      | ~ A ),
    inference(rewrite,[status(thm)],[1327,267]) ).

thf(1389,plain,
    ! [C: bool,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
       != ( huffma2021818691e_Leaf @ $o @ A @ ( pp @ C ) ) )
      | ~ ( pp @ C ) ),
    inference(prim_subst,[status(thm)],[1372:[bind(A,$thf( pp @ D ))]]) ).

thf(1406,plain,
    ! [C: bool,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
       != ( huffma2021818691e_Leaf @ $o @ A @ ( pp @ C ) ) )
      | ~ ( pp @ C ) ),
    inference(simp,[status(thm)],[1389]) ).

thf(643,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ D ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( B
       != ( huffma83463279weight @ a @ t_2 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(644,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma83463279weight @ a @ t_2 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ C ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( A )),bind(B,$thf( huffma83463279weight @ a @ t_2 )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(655,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma83463279weight @ a @ t_2 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ C ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[644]) ).

thf(1064,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ A )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C
       != ( huffma1134658180e_cost @ a @ t_2 ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1065,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ A )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1064:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma1134658180e_cost @ a @ t_2 )),bind(D,$thf( D ))]]) ).

thf(1158,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ A )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1065]) ).

thf(29,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ~ ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
         => ~ ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_inf1E) ).

thf(217,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ~ ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
         => ~ ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(50,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
     => ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
         => ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_IntE) ).

thf(276,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
     => ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
         => ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(24,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

thf(202,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(1373,plain,
    ! [B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
     != ( huffma2021818691e_Leaf @ $o @ A @ $true ) ),
    inference(simp,[status(thm)],[1372]) ).

thf(1405,plain,
    ! [B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
     != ( huffma2021818691e_Leaf @ $o @ A @ $true ) ),
    inference(simp,[status(thm)],[1373]) ).

thf(1409,plain,
    ! [F: nat,E: nat,D: nat,C: huffma1450048681e_tree @ $o,B: nat,A: huffma1450048681e_tree @ $o] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ A ) )
      | ( A
       != ( huffma2021818691e_Leaf @ $o @ E @ $true ) )
      | ( C
       != ( huffma2021818691e_Leaf @ $o @ F @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[157,1405]) ).

thf(1410,plain,
    ! [E: nat,D: nat,C: nat,B: nat,A: huffma1450048681e_tree @ $o] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ C @ ( huffma2021818691e_Leaf @ $o @ E @ $false ) )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ A ) )
      | ( A
       != ( huffma2021818691e_Leaf @ $o @ D @ $true ) ) ),
    inference(pattern_uni,[status(thm)],[1409:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma2021818691e_Leaf @ $o @ G @ $false )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G ))]]) ).

thf(1426,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ ( huffma2021818691e_Leaf @ $o @ D @ $false ) )
     != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ A @ ( huffma2021818691e_Leaf @ $o @ C @ $true ) ) ),
    inference(simp,[status(thm)],[1410]) ).

thf(85,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

thf(384,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(4,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(140,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(141,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(cnf,[status(esa)],[140]) ).

thf(142,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(lifteq,[status(thm)],[141]) ).

thf(72,axiom,
    lattice @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).

thf(350,plain,
    lattice @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(562,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ ( fun @ TA @ TB ) )
      | ( ( lattice @ bool )
       != ( lattice @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[350,146]) ).

thf(563,plain,
    ! [TA: $tType] : ( lattice @ ( fun @ TA @ bool ) ),
    inference(pattern_uni,[status(thm)],[562:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( bool ))]]) ).

thf(568,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( lattice @ ( fun @ TB @ TC ) )
      | ( ( lattice @ ( fun @ TA @ bool ) )
       != ( lattice @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[563,146]) ).

thf(569,plain,
    ! [TA: $tType,TB: $tType] : ( lattice @ ( fun @ TB @ ( fun @ TA @ bool ) ) ),
    inference(pattern_uni,[status(thm)],[568:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( fun @ TA @ bool ))]]) ).

thf(572,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( lattice @ ( fun @ TC @ TD ) )
      | ( ( lattice @ ( fun @ TB @ ( fun @ TA @ bool ) ) )
       != ( lattice @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[569,146]) ).

thf(573,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( lattice @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ),
    inference(pattern_uni,[status(thm)],[572:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( fun @ TB @ ( fun @ TA @ bool ) ))]]) ).

thf(583,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( lattice @ ( fun @ TD @ TE ) )
      | ( ( lattice @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) )
       != ( lattice @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[573,146]) ).

thf(584,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( lattice @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[583:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ))]]) ).

thf(594,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( lattice @ ( fun @ TE @ TF ) )
      | ( ( lattice @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) )
       != ( lattice @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[584,146]) ).

thf(595,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( lattice @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[594:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ))]]) ).

thf(598,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( lattice @ ( fun @ TF @ TG ) )
      | ( ( lattice @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) )
       != ( lattice @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[595,146]) ).

thf(599,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( lattice @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[598:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ))]]) ).

thf(605,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( lattice @ ( fun @ TG @ TH ) )
      | ( ( lattice @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) )
       != ( lattice @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[599,146]) ).

thf(606,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( lattice @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[605:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ))]]) ).

thf(609,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( lattice @ ( fun @ TH @ TI ) )
      | ( ( lattice @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) )
       != ( lattice @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[606,146]) ).

thf(610,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( lattice @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[609:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ))]]) ).

thf(668,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( lattice @ ( fun @ TI @ TJ ) )
      | ( ( lattice @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) )
       != ( lattice @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[610,146]) ).

thf(669,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( lattice @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[668:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ))]]) ).

thf(672,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( lattice @ ( fun @ TJ @ TK ) )
      | ( ( lattice @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[669,146]) ).

thf(673,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( lattice @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[672:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ))]]) ).

thf(1344,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( lattice @ ( fun @ TK @ TL ) )
      | ( ( lattice @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[673,146]) ).

thf(1345,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( lattice @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1344:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1360,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( lattice @ ( fun @ TL @ TM ) )
      | ( ( lattice @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[1345,146]) ).

thf(1361,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( lattice @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1360:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1437,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( lattice @ ( fun @ TM @ TN ) )
      | ( ( lattice @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[1361,146]) ).

thf(1438,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( lattice @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1437:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1721,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( lattice @ ( fun @ TN @ TO ) )
      | ( ( lattice @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[1438,146]) ).

thf(1722,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( lattice @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1721:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1737,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( lattice @ ( fun @ TO @ TP ) )
      | ( ( lattice @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TP ) ) ),
    inference(paramod_ordered,[status(thm)],[1722,146]) ).

thf(1738,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( lattice @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1737:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2149,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( lattice @ ( fun @ TP @ TQ ) )
      | ( ( lattice @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TQ ) ) ),
    inference(paramod_ordered,[status(thm)],[1738,146]) ).

thf(2150,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( lattice @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2149:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2165,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( lattice @ ( fun @ TQ @ TR ) )
      | ( ( lattice @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TR ) ) ),
    inference(paramod_ordered,[status(thm)],[2150,146]) ).

thf(2166,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( lattice @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2165:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2242,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( lattice @ ( fun @ TR @ TS ) )
      | ( ( lattice @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TS ) ) ),
    inference(paramod_ordered,[status(thm)],[2166,146]) ).

thf(2243,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( lattice @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2242:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2295,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( lattice @ ( fun @ TS @ TT ) )
      | ( ( lattice @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TT ) ) ),
    inference(paramod_ordered,[status(thm)],[2243,146]) ).

thf(2296,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( lattice @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2295:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2311,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( lattice @ ( fun @ TT @ TU ) )
      | ( ( lattice @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TU ) ) ),
    inference(paramod_ordered,[status(thm)],[2296,146]) ).

thf(2312,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( lattice @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2311:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2860,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( lattice @ ( fun @ TU @ TV ) )
      | ( ( lattice @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TV ) ) ),
    inference(paramod_ordered,[status(thm)],[2312,146]) ).

thf(2861,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( lattice @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2860:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2882,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( lattice @ ( fun @ TV @ TW ) )
      | ( ( lattice @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TW ) ) ),
    inference(paramod_ordered,[status(thm)],[2861,146]) ).

thf(2883,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( lattice @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2882:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(2978,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( lattice @ ( fun @ TW @ TX ) )
      | ( ( lattice @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TX ) ) ),
    inference(paramod_ordered,[status(thm)],[2883,146]) ).

thf(2979,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( lattice @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2978:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3385,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( lattice @ ( fun @ TX @ TY ) )
      | ( ( lattice @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TY ) ) ),
    inference(paramod_ordered,[status(thm)],[2979,146]) ).

thf(3386,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( lattice @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3385:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3407,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( lattice @ ( fun @ TY @ TZ ) )
      | ( ( lattice @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZ ) ) ),
    inference(paramod_ordered,[status(thm)],[3386,146]) ).

thf(3408,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( lattice @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3407:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3851,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( lattice @ ( fun @ TZ @ TZA ) )
      | ( ( lattice @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZA ) ) ),
    inference(paramod_ordered,[status(thm)],[3408,146]) ).

thf(3852,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( lattice @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3851:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(3883,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( lattice @ ( fun @ TZA @ TZB ) )
      | ( ( lattice @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZB ) ) ),
    inference(paramod_ordered,[status(thm)],[3852,146]) ).

thf(3884,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( lattice @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[3883:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(4403,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( lattice @ ( fun @ TZB @ TZC ) )
      | ( ( lattice @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZC ) ) ),
    inference(paramod_ordered,[status(thm)],[3884,146]) ).

thf(4404,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( lattice @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4403:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(4969,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
      ( ( lattice @ ( fun @ TZC @ TZD ) )
      | ( ( lattice @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZD ) ) ),
    inference(paramod_ordered,[status(thm)],[4404,146]) ).

thf(4970,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( lattice @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4969:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(5457,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
      ( ( lattice @ ( fun @ TZD @ TZE ) )
      | ( ( lattice @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZE ) ) ),
    inference(paramod_ordered,[status(thm)],[4970,146]) ).

thf(5458,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( lattice @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5457:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(5583,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
      ( ( lattice @ ( fun @ TZE @ TZF ) )
      | ( ( lattice @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZF ) ) ),
    inference(paramod_ordered,[status(thm)],[5458,146]) ).

thf(5584,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( lattice @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5583:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(5955,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
      ( ( lattice @ ( fun @ TZF @ TZG ) )
      | ( ( lattice @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZG ) ) ),
    inference(paramod_ordered,[status(thm)],[5584,146]) ).

thf(5956,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( lattice @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5955:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(6411,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
      ( ( lattice @ ( fun @ TZG @ TZH ) )
      | ( ( lattice @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZH ) ) ),
    inference(paramod_ordered,[status(thm)],[5956,146]) ).

thf(6412,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( lattice @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6411:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(6898,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
      ( ( lattice @ ( fun @ TZH @ TZI ) )
      | ( ( lattice @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZI ) ) ),
    inference(paramod_ordered,[status(thm)],[6412,146]) ).

thf(6899,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( lattice @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6898:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(7465,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
      ( ( lattice @ ( fun @ TZI @ TZJ ) )
      | ( ( lattice @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZJ ) ) ),
    inference(paramod_ordered,[status(thm)],[6899,146]) ).

thf(7466,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( lattice @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[7465:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(7599,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
      ( ( lattice @ ( fun @ TZJ @ TZK ) )
      | ( ( lattice @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZK ) ) ),
    inference(paramod_ordered,[status(thm)],[7466,146]) ).

thf(7600,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( lattice @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[7599:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(8041,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
      ( ( lattice @ ( fun @ TZK @ TZL ) )
      | ( ( lattice @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZL ) ) ),
    inference(paramod_ordered,[status(thm)],[7600,146]) ).

thf(8042,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( lattice @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8041:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(8621,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] :
      ( ( lattice @ ( fun @ TZL @ TZM ) )
      | ( ( lattice @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZM ) ) ),
    inference(paramod_ordered,[status(thm)],[8042,146]) ).

thf(8622,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] : ( lattice @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8621:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

thf(500,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(1076,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ A @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1077,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ A @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1076:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) )),bind(D,$thf( D ))]]) ).

thf(1164,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ A @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1077]) ).

thf(17,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
     => ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
       => ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_inf1I) ).

thf(184,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
     => ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
       => ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(185,plain,
    ! [TA: $tType,C: fun @ TA @ bool,B: TA,A: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
      | ~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
      | ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[184]) ).

thf(27,axiom,
    bounded_lattice @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).

thf(210,plain,
    bounded_lattice @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(13,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounded_lattice @ ( fun @ TB @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).

thf(175,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounded_lattice @ ( fun @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(176,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ ( bounded_lattice @ TB )
      | ( bounded_lattice @ ( fun @ TA @ TB ) ) ),
    inference(cnf,[status(esa)],[175]) ).

thf(3839,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ ( fun @ TA @ TB ) )
      | ( ( bounded_lattice @ bool )
       != ( bounded_lattice @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[210,176]) ).

thf(3840,plain,
    ! [TA: $tType] : ( bounded_lattice @ ( fun @ TA @ bool ) ),
    inference(pattern_uni,[status(thm)],[3839:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( bool ))]]) ).

thf(3871,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( bounded_lattice @ ( fun @ TB @ TC ) )
      | ( ( bounded_lattice @ ( fun @ TA @ bool ) )
       != ( bounded_lattice @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[3840,176]) ).

thf(3872,plain,
    ! [TA: $tType,TB: $tType] : ( bounded_lattice @ ( fun @ TB @ ( fun @ TA @ bool ) ) ),
    inference(pattern_uni,[status(thm)],[3871:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( fun @ TA @ bool ))]]) ).

thf(4385,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( bounded_lattice @ ( fun @ TC @ TD ) )
      | ( ( bounded_lattice @ ( fun @ TB @ ( fun @ TA @ bool ) ) )
       != ( bounded_lattice @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[3872,176]) ).

thf(4386,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( bounded_lattice @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ),
    inference(pattern_uni,[status(thm)],[4385:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( fun @ TB @ ( fun @ TA @ bool ) ))]]) ).

thf(4423,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( bounded_lattice @ ( fun @ TD @ TE ) )
      | ( ( bounded_lattice @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) )
       != ( bounded_lattice @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[4386,176]) ).

thf(4424,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( bounded_lattice @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4423:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ))]]) ).

thf(4993,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( bounded_lattice @ ( fun @ TE @ TF ) )
      | ( ( bounded_lattice @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) )
       != ( bounded_lattice @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[4424,176]) ).

thf(4994,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( bounded_lattice @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4993:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ))]]) ).

thf(5481,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( bounded_lattice @ ( fun @ TF @ TG ) )
      | ( ( bounded_lattice @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) )
       != ( bounded_lattice @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[4994,176]) ).

thf(5482,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( bounded_lattice @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5481:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ))]]) ).

thf(5937,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( bounded_lattice @ ( fun @ TG @ TH ) )
      | ( ( bounded_lattice @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) )
       != ( bounded_lattice @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[5482,176]) ).

thf(5938,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( bounded_lattice @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5937:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ))]]) ).

thf(63,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
    <=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).

thf(320,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA] :
      ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
       => ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
      & ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
       => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(6393,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( bounded_lattice @ ( fun @ TH @ TI ) )
      | ( ( bounded_lattice @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[5938,176]) ).

thf(6394,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( bounded_lattice @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6393:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ))]]) ).

thf(6482,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( bounded_lattice @ ( fun @ TI @ TJ ) )
      | ( ( bounded_lattice @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[6394,176]) ).

thf(6483,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( bounded_lattice @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6482:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ))]]) ).

thf(1417,plain,
    ! [F: nat,E: nat,D: nat,C: huffma1450048681e_tree @ $o,B: nat,A: huffma1450048681e_tree @ $o] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ A ) )
      | ( C
       != ( huffma2021818691e_Leaf @ $o @ E @ $true ) )
      | ( A
       != ( huffma2021818691e_Leaf @ $o @ F @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[157,1405]) ).

thf(1418,plain,
    ! [E: nat,D: nat,C: nat,B: huffma1450048681e_tree @ $o,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ C @ B )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ A @ ( huffma2021818691e_Leaf @ $o @ E @ $false ) ) )
      | ( B
       != ( huffma2021818691e_Leaf @ $o @ D @ $true ) ) ),
    inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( huffma2021818691e_Leaf @ $o @ G @ $false )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G ))]]) ).

thf(1430,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ ( huffma2021818691e_Leaf @ $o @ C @ $true ) )
     != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ A @ ( huffma2021818691e_Leaf @ $o @ D @ $false ) ) ),
    inference(simp,[status(thm)],[1418]) ).

thf(1004,plain,
    ! [D: nat,C: bool,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ D @ C )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ C )
      | ( A != fFalse ) ),
    inference(paramod_ordered,[status(thm)],[157,267]) ).

thf(1005,plain,
    ! [C: nat,B: bool,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ B )
       != ( huffma2021818691e_Leaf @ bool @ A @ fFalse ) )
      | ~ ( pp @ B ) ),
    inference(pattern_uni,[status(thm)],[1004:[bind(A,$thf( fFalse ))]]) ).

thf(1330,plain,
    ! [C: nat,B: bool,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ B )
       != ( huffma2021818691e_Leaf @ bool @ A @ fFalse ) )
      | ~ ( pp @ B ) ),
    inference(simp,[status(thm)],[1005]) ).

thf(21,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ A )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_inf_Ocommute) ).

thf(194,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ A )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(195,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ~ ( semilattice_inf @ TA )
      | ( ( inf_inf @ TA @ B @ A )
        = ( inf_inf @ TA @ A @ B ) ) ),
    inference(cnf,[status(esa)],[194]) ).

thf(196,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( ( inf_inf @ TA @ B @ A )
        = ( inf_inf @ TA @ A @ B ) )
      | ~ ( semilattice_inf @ TA ) ),
    inference(lifteq,[status(thm)],[195]) ).

thf(132,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
      ( ( huffma2021818691e_Leaf @ TA @ E @ D )
     != ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_tree_Osimps_I3_J) ).

thf(542,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
      ( ( huffma2021818691e_Leaf @ TA @ E @ D )
     != ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(107,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma1280178957ee_rec @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_tree_Orecs_I1_J) ).

thf(460,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma1280178957ee_rec @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(5,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounded_lattice_bot @ ( fun @ TB @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).

thf(143,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounded_lattice_bot @ ( fun @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(144,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ ( bounded_lattice @ TB )
      | ( bounded_lattice_bot @ ( fun @ TA @ TB ) ) ),
    inference(cnf,[status(esa)],[143]) ).

thf(558,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TA @ TB ) )
      | ( ( bounded_lattice @ bool )
       != ( bounded_lattice @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[210,144]) ).

thf(559,plain,
    ! [TA: $tType] : ( bounded_lattice_bot @ ( fun @ TA @ bool ) ),
    inference(pattern_uni,[status(thm)],[558:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( bool ))]]) ).

thf(19,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Int__left__absorb) ).

thf(189,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(6395,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TH @ TI ) )
      | ( ( bounded_lattice @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[5938,144]) ).

thf(6396,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( bounded_lattice_bot @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6395:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ))]]) ).

thf(53,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA] :
    ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_exists__in__alphabet) ).

thf(284,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA] :
    ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(96,axiom,
    ! [A: nat,B: nat] :
      ( ( plus_plus @ nat @ B @ A )
      = ( plus_plus @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_nat__add__commute) ).

thf(416,plain,
    ! [A: nat,B: nat] :
      ( ( plus_plus @ nat @ B @ A )
      = ( plus_plus @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(6922,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( bounded_lattice @ ( fun @ TJ @ TK ) )
      | ( ( bounded_lattice @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[6483,176]) ).

thf(6923,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( bounded_lattice @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6922:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ))]]) ).

thf(32,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ TA @ bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_inf1D2) ).

thf(228,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ TA @ bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(55,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( ( bot_bot @ ( fun @ TA @ bool ) )
        = ( collect @ TA @ A ) )
    <=> ! [B: TA] :
          ~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_empty__Collect__eq) ).

thf(289,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
          = ( collect @ TA @ A ) )
       => ! [B: TA] :
            ~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
      & ( ! [B: TA] :
            ~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
       => ( ( bot_bot @ ( fun @ TA @ bool ) )
          = ( collect @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(44,axiom,
    ! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_consistent_Osimps_I1_J) ).

thf(261,plain,
    ! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(111,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ A @ B ) )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_add__right__cancel) ).

thf(475,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ( plus_plus @ TA @ C @ B )
              = ( plus_plus @ TA @ A @ B ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( plus_plus @ TA @ C @ B )
              = ( plus_plus @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(10,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TB )
     => ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
          ( ( aa @ TA @ TB @ ( inf_inf @ ( fun @ TA @ TB ) @ B @ A ) @ C )
          = ( inf_inf @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_inf__fun__def) ).

thf(162,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TB )
     => ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
          ( ( aa @ TA @ TB @ ( inf_inf @ ( fun @ TA @ TB ) @ B @ A ) @ C )
          = ( inf_inf @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(163,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: fun @ TB @ TA,A: fun @ TB @ TA] :
      ( ~ ( lattice @ TA )
      | ( ( aa @ TB @ TA @ ( inf_inf @ ( fun @ TB @ TA ) @ B @ A ) @ C )
        = ( inf_inf @ TA @ ( aa @ TB @ TA @ B @ C ) @ ( aa @ TB @ TA @ A @ C ) ) ) ),
    inference(cnf,[status(esa)],[162]) ).

thf(164,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: fun @ TB @ TA,A: fun @ TB @ TA] :
      ( ( ( aa @ TB @ TA @ ( inf_inf @ ( fun @ TB @ TA ) @ B @ A ) @ C )
        = ( inf_inf @ TA @ ( aa @ TB @ TA @ B @ C ) @ ( aa @ TB @ TA @ A @ C ) ) )
      | ~ ( lattice @ TA ) ),
    inference(lifteq,[status(thm)],[163]) ).

thf(28,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ! [B: TA] :
          ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
    <=> ( A
        = ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_all__not__in__conv) ).

thf(211,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( ! [B: TA] :
            ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
       => ( A
          = ( bot_bot @ ( fun @ TA @ bool ) ) ) )
      & ( ( A
          = ( bot_bot @ ( fun @ TA @ bool ) ) )
       => ! [B: TA] :
            ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(114,axiom,
    ! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
      ( ( huffma1146269203erNode @ TA @ E @ D @ C )
     != ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_tree_Osimps_I4_J) ).

thf(485,plain,
    ! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
      ( ( huffma1146269203erNode @ TA @ E @ D @ C )
     != ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(36,axiom,
    bounded_lattice_bot @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).

thf(238,plain,
    bounded_lattice_bot @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(74,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

thf(353,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(7491,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TK @ TL ) )
      | ( ( bounded_lattice @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[6923,144]) ).

thf(7492,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( bounded_lattice_bot @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[7491:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ))]]) ).

thf(7,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_inf__idem) ).

thf(147,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(4995,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TE @ TF ) )
      | ( ( bounded_lattice @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) )
       != ( bounded_lattice @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[4424,144]) ).

thf(4996,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( bounded_lattice_bot @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4995:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ))]]) ).

thf(88,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ A @ B ) )
         => ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__right__imp__eq) ).

thf(396,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ A @ B ) )
         => ( C = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(649,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ D @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( B
       != ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(650,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[649:[bind(A,$thf( A )),bind(B,$thf( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(660,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[650]) ).

thf(99,axiom,
    ab_semigroup_add @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).

thf(428,plain,
    ab_semigroup_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(60,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(312,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(633,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ B @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( D
       != ( huffma83463279weight @ a @ t_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(634,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ ( huffma83463279weight @ a @ t_1 ) @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ B @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[633:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( huffma83463279weight @ a @ t_1 ))]]) ).

thf(34,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_empty__iff) ).

thf(233,plain,
    ! [TA: $tType,A: TA] :
      ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(40,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
    <=> ( A
       != ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ex__in__conv) ).

thf(248,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
       => ( A
         != ( bot_bot @ ( fun @ TA @ bool ) ) ) )
      & ( ( A
         != ( bot_bot @ ( fun @ TA @ bool ) ) )
       => ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(83,axiom,
    semiring_1 @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).

thf(380,plain,
    semiring_1 @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(102,axiom,
    ! [TA: $tType,A: nat,B: TA,C: TA] :
      ( ( ( C = B )
       => ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
          = A ) )
      & ( ( C != B )
       => ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
          = ( zero_zero @ nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_freq_Osimps_I1_J) ).

thf(439,plain,
    ! [TA: $tType,A: nat,B: TA,C: TA] :
      ( ( ( C = B )
       => ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
          = A ) )
      & ( ( C != B )
       => ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
          = ( zero_zero @ nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1002,plain,
    ! [D: nat,C: $o,B: nat,A: $o] :
      ( ( ( huffma2021818691e_Leaf @ $o @ D @ C )
       != ( huffma2021818691e_Leaf @ $o @ B @ A ) )
      | ~ C
      | ( A
       != ( pp @ fFalse ) ) ),
    inference(paramod_ordered,[status(thm)],[157,267]) ).

thf(1003,plain,
    ! [C: nat,B: $o,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ C @ B )
       != ( huffma2021818691e_Leaf @ $o @ A @ ( pp @ fFalse ) ) )
      | ~ B ),
    inference(pattern_uni,[status(thm)],[1002:[bind(A,$thf( pp @ fFalse )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(1329,plain,
    ! [C: nat,B: $o,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ C @ B )
       != ( huffma2021818691e_Leaf @ $o @ A @ ( pp @ fFalse ) ) )
      | ~ B ),
    inference(simp,[status(thm)],[1003]) ).

thf(2177,plain,
    ! [C: nat,B: $o,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ C @ B )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) )
      | ~ B ),
    inference(rewrite,[status(thm)],[1329,267]) ).

thf(2194,plain,
    ! [C: bool,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ B @ ( pp @ C ) )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) )
      | ~ ( pp @ C ) ),
    inference(prim_subst,[status(thm)],[2177:[bind(A,$thf( A )),bind(B,$thf( pp @ D ))]]) ).

thf(2204,plain,
    ! [C: bool,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ B @ ( pp @ C ) )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) )
      | ~ ( pp @ C ) ),
    inference(simp,[status(thm)],[2194]) ).

thf(129,axiom,
    ! [TA: $tType,A: TA,B: nat] :
      ( ( huffma1134658180e_cost @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_cost_Osimps_I1_J) ).

thf(529,plain,
    ! [TA: $tType,A: TA,B: nat] :
      ( ( huffma1134658180e_cost @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(1054,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ A @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
      | ( C != w ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1055,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ w )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ A @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1054:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( w ))]]) ).

thf(1153,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ w )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ A @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1055]) ).

thf(84,axiom,
    ! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_tree_Osimps_I6_J) ).

thf(381,plain,
    ! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(30,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TB )
     => ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
          ( ( aa @ TA @ TB @ ( inf_inf @ ( fun @ TA @ TB ) @ C @ B ) @ A )
          = ( inf_inf @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_inf__apply) ).

thf(220,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TB )
     => ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
          ( ( aa @ TA @ TB @ ( inf_inf @ ( fun @ TA @ TB ) @ C @ B ) @ A )
          = ( inf_inf @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(23,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(200,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(201,plain,
    ! [B: bool,A: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[200]) ).

thf(1074,plain,
    ! [D: nat,C: huffma1450048681e_tree @ a,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ A ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C != t_1 ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1075,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_1 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ A ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 ))]]) ).

thf(1163,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_1 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ A ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1075]) ).

thf(3,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( collect @ TA @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).

thf(137,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( collect @ TA @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(138,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( collect @ TA @ A )
      = A ),
    inference(cnf,[status(esa)],[137]) ).

thf(139,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( collect @ TA @ A )
      = A ),
    inference(lifteq,[status(thm)],[138]) ).

thf(31,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( fun @ TA @ bool ) ) )
    <=> ! [B: TA] :
          ~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__empty__eq) ).

thf(223,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( ( ( collect @ TA @ A )
          = ( bot_bot @ ( fun @ TA @ bool ) ) )
       => ! [B: TA] :
            ~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
      & ( ! [B: TA] :
            ~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
       => ( ( collect @ TA @ A )
          = ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(225,plain,
    ! [TA: $tType,B: TA,A: fun @ TA @ bool] :
      ( ( ( collect @ TA @ A )
       != ( bot_bot @ ( fun @ TA @ bool ) ) )
      | ~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
    inference(cnf,[status(esa)],[223]) ).

thf(227,plain,
    ! [TA: $tType,B: TA,A: fun @ TA @ bool] :
      ( ( ( collect @ TA @ A )
       != ( bot_bot @ ( fun @ TA @ bool ) ) )
      | ~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
    inference(lifteq,[status(thm)],[225]) ).

thf(577,plain,
    ! [TB: $tType,C: TB,B: fun @ TB @ bool,A: fun @ TB @ bool] :
      ( ( A
       != ( bot_bot @ ( fun @ TB @ bool ) ) )
      | ~ ( pp @ ( aa @ TB @ bool @ B @ C ) )
      | ( ( collect @ TB @ A )
       != ( collect @ TB @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[139,227]) ).

thf(578,plain,
    ! [TB: $tType,B: TB,A: fun @ TB @ bool] :
      ( ( A
       != ( bot_bot @ ( fun @ TB @ bool ) ) )
      | ~ ( pp @ ( aa @ TB @ bool @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[577:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(580,plain,
    ! [TA: $tType,A: TA] :
      ~ ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ),
    inference(simp,[status(thm)],[578]) ).

thf(790,plain,
    ! [TB: $tType,E: TB,D: nat,C: bool,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ D @ C )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ C )
      | ( A
       != ( aa @ TB @ bool @ ( bot_bot @ ( fun @ TB @ bool ) ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[157,580]) ).

thf(791,plain,
    ! [TB: $tType,D: TB,C: nat,B: bool,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ B )
       != ( huffma2021818691e_Leaf @ bool @ A @ ( aa @ TB @ bool @ ( bot_bot @ ( fun @ TB @ bool ) ) @ D ) ) )
      | ~ ( pp @ B ) ),
    inference(pattern_uni,[status(thm)],[790:[bind(A,$thf( aa @ TB @ bool @ ( bot_bot @ ( fun @ TB @ bool ) ) @ G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).

thf(1223,plain,
    ! [TA: $tType,D: TA,C: nat,B: bool,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ B )
       != ( huffma2021818691e_Leaf @ bool @ A @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ D ) ) )
      | ~ ( pp @ B ) ),
    inference(simp,[status(thm)],[791]) ).

thf(9,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
    <=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
        & ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Int__iff) ).

thf(158,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
       => ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
          & ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
      & ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
          & ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
       => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(160,plain,
    ! [TA: $tType,C: TA,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
      | ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
    inference(cnf,[status(esa)],[158]) ).

thf(100,axiom,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
          = ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(429,plain,
    ! [TA: $tType] :
      ( ( ab_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
          = ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(11,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
      = ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Int__def) ).

thf(165,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
      = ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(20,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_emptyE) ).

thf(192,plain,
    ! [TA: $tType,A: TA] :
      ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(629,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ B @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( D
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(630,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ B @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[629:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ))]]) ).

thf(22,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
      = ( bot_bot @ ( fun @ TA @ bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Int__empty__right) ).

thf(197,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
      = ( bot_bot @ ( fun @ TA @ bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(7489,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( bounded_lattice @ ( fun @ TK @ TL ) )
      | ( ( bounded_lattice @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[6923,176]) ).

thf(7490,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( bounded_lattice @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[7489:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ))]]) ).

thf(8025,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TL @ TM ) )
      | ( ( bounded_lattice @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[7490,144]) ).

thf(8026,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( bounded_lattice_bot @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8025:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(128,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
      ( ( huffma1518433673istent @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
    <=> ( ( huffma1518433673istent @ TA @ B )
        & ( huffma1518433673istent @ TA @ A )
        & ( ( inf_inf @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) )
          = ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_consistent_Osimps_I2_J) ).

thf(522,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
      ( ( ( huffma1518433673istent @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
       => ( ( huffma1518433673istent @ TA @ B )
          & ( huffma1518433673istent @ TA @ A )
          & ( ( inf_inf @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) )
            = ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
      & ( ( ( huffma1518433673istent @ TA @ B )
          & ( huffma1518433673istent @ TA @ A )
          & ( ( inf_inf @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) )
            = ( bot_bot @ ( fun @ TA @ bool ) ) ) )
       => ( huffma1518433673istent @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(1066,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( A
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1067,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( A
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1066:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )),bind(D,$thf( D ))]]) ).

thf(1159,plain,
    ! [B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ nat @ B @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
     != ( huffma2021818691e_Leaf @ nat @ A @ ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1067]) ).

thf(117,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
      ( ( huffma83463279weight @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma83463279weight @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weight_Osimps_I2_J) ).

thf(493,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
      ( ( huffma83463279weight @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma83463279weight @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(105,axiom,
    cancel_semigroup_add @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).

thf(456,plain,
    cancel_semigroup_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(125,axiom,
    huffma1518433673istent @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InnerNode_Oprems) ).

thf(519,plain,
    huffma1518433673istent @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(62,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_inf__sup__aci_I4_J) ).

thf(317,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(1000,plain,
    ! [D: nat,C: bool,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ D @ C )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ A )
      | ( C != fFalse ) ),
    inference(paramod_ordered,[status(thm)],[157,267]) ).

thf(1001,plain,
    ! [C: nat,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ fFalse )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ A ) ),
    inference(pattern_uni,[status(thm)],[1000:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( fFalse ))]]) ).

thf(1328,plain,
    ! [C: nat,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ fFalse )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ A ) ),
    inference(simp,[status(thm)],[1001]) ).

thf(8023,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( bounded_lattice @ ( fun @ TL @ TM ) )
      | ( ( bounded_lattice @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[7490,176]) ).

thf(8024,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( bounded_lattice @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8023:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(8603,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( bounded_lattice @ ( fun @ TM @ TN ) )
      | ( ( bounded_lattice @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[8024,176]) ).

thf(8604,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( bounded_lattice @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8603:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(75,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Int__absorb) ).

thf(356,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(119,axiom,
    semilattice_inf @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).

thf(499,plain,
    semilattice_inf @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(66,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_inf_Oidem) ).

thf(328,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(1068,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ A ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C
       != ( huffma83463279weight @ a @ t_2 ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1069,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma83463279weight @ a @ t_2 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ A ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1068:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma83463279weight @ a @ t_2 )),bind(D,$thf( D ))]]) ).

thf(1160,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma83463279weight @ a @ t_2 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ A ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1069]) ).

thf(115,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
      ( ( huffma1134658180e_cost @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma1134658180e_cost @ TA @ B ) ) @ ( huffma83463279weight @ TA @ A ) ) @ ( huffma1134658180e_cost @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cost_Osimps_I2_J) ).

thf(488,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
      ( ( huffma1134658180e_cost @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma1134658180e_cost @ TA @ B ) ) @ ( huffma83463279weight @ TA @ A ) ) @ ( huffma1134658180e_cost @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(193,plain,
    ! [TA: $tType,A: TA] :
      ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
    inference(cnf,[status(esa)],[192]) ).

thf(8742,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TN @ TO ) )
      | ( ( bounded_lattice @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[8604,144]) ).

thf(8743,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( bounded_lattice_bot @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8742:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1058,plain,
    ! [D: nat,C: huffma1450048681e_tree @ a,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ A )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
      | ( C
       != ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1059,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ A )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma1146269203erNode @ a @ w @ t_1 @ t_2 )),bind(D,$thf( D ))]]) ).

thf(1155,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ A )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1059]) ).

thf(9259,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] :
      ( ( lattice @ ( fun @ TZM @ TZN ) )
      | ( ( lattice @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( lattice @ TZN ) ) ),
    inference(paramod_ordered,[status(thm)],[8622,146]) ).

thf(9260,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] : ( lattice @ ( fun @ TZM @ ( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[9259:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( TZM )),bind_type(TZN,$thf( fun @ TZL @ ( fun @ TZK @ ( fun @ TZJ @ ( fun @ TZI @ ( fun @ TZH @ ( fun @ TZG @ ( fun @ TZF @ ( fun @ TZE @ ( fun @ TZD @ ( fun @ TZC @ ( fun @ TZB @ ( fun @ TZA @ ( fun @ TZ @ ( fun @ TY @ ( fun @ TX @ ( fun @ TW @ ( fun @ TV @ ( fun @ TU @ ( fun @ TT @ ( fun @ TS @ ( fun @ TR @ ( fun @ TQ @ ( fun @ TP @ ( fun @ TO @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(621,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ B )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( D
       != ( huffma1134658180e_cost @ a @ t_2 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(622,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ t_2 ) @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ B )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[621:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( huffma1134658180e_cost @ a @ t_2 ))]]) ).

thf(87,axiom,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
        = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_of__nat__0) ).

thf(393,plain,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
        = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(106,axiom,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ C @ A ) )
         => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__imp__eq) ).

thf(457,plain,
    ! [TA: $tType] :
      ( ( cancel146912293up_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ C @ A ) )
         => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(1126,plain,
    ! [TB: $tType,F: TB,E: fun @ TB @ bool,D: nat,C: fun @ TB @ bool,B: nat,A: fun @ TB @ bool] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ B @ A ) )
      | ( A
       != ( bot_bot @ ( fun @ TB @ bool ) ) )
      | ~ ( pp @ ( aa @ TB @ bool @ E @ F ) )
      | ( C
       != ( collect @ TB @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[157,227]) ).

thf(1127,plain,
    ! [TB: $tType,E: fun @ TB @ bool,D: TB,C: nat,B: nat,A: fun @ TB @ bool] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ C @ ( collect @ TB @ E ) )
       != ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ B @ A ) )
      | ( A
       != ( bot_bot @ ( fun @ TB @ bool ) ) )
      | ~ ( pp @ ( aa @ TB @ bool @ E @ D ) ) ),
    inference(pattern_uni,[status(thm)],[1126:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( collect @ TB @ G )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).

thf(1189,plain,
    ! [TA: $tType,D: fun @ TA @ bool,C: TA,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TA @ bool ) @ B @ ( collect @ TA @ D ) )
       != ( huffma2021818691e_Leaf @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
      | ~ ( pp @ ( aa @ TA @ bool @ D @ C ) ) ),
    inference(simp,[status(thm)],[1127]) ).

thf(8048,plain,
    ! [TA: $tType,D: fun @ TA @ bool,C: TA,B: nat,A: nat] :
      ( ( B != A )
      | ( ( collect @ TA @ D )
       != ( bot_bot @ ( fun @ TA @ bool ) ) )
      | ~ ( pp @ ( aa @ TA @ bool @ D @ C ) ) ),
    inference(simp,[status(thm)],[1189]) ).

thf(8093,plain,
    ! [TA: $tType,B: fun @ TA @ bool,A: TA] :
      ( ( ( collect @ TA @ B )
       != ( bot_bot @ ( fun @ TA @ bool ) ) )
      | ~ ( pp @ ( aa @ TA @ bool @ B @ A ) ) ),
    inference(simp,[status(thm)],[8048]) ).

thf(8481,plain,
    ! [TA: $tType,D: fun @ TA @ bool,C: TA,B: bool,A: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( ( collect @ TA @ D )
       != ( bot_bot @ ( fun @ TA @ bool ) ) )
      | ( ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
       != ( pp @ ( aa @ TA @ bool @ D @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[201,8093]) ).

thf(8482,plain,
    ! [B: bool,A: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( ( collect @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) )
       != ( bot_bot @ ( fun @ bool @ bool ) ) ) ),
    inference(pattern_uni,[status(thm)],[8481:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ F )),bind_type(TA,$thf( bool ))]]) ).

thf(8579,plain,
    ! [B: bool,A: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( ( collect @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) )
       != ( bot_bot @ ( fun @ bool @ bool ) ) ) ),
    inference(simp,[status(thm)],[8482]) ).

thf(8677,plain,
    ! [B: bool,A: bool] :
      ( ~ ( pp @ B )
      | ( ( collect @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) )
       != ( bot_bot @ ( fun @ bool @ bool ) ) )
      | ( ( pp @ A )
       != ( pp @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[8579]) ).

thf(8679,plain,
    ! [A: bool] :
      ( ~ ( pp @ A )
      | ( ( collect @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) )
       != ( bot_bot @ ( fun @ bool @ bool ) ) ) ),
    inference(pattern_uni,[status(thm)],[8677:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(8721,plain,
    ! [B: bool,A: fun @ bool @ bool] :
      ( ~ ( pp @ B )
      | ( A
       != ( bot_bot @ ( fun @ bool @ bool ) ) )
      | ( ( collect @ bool @ A )
       != ( collect @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[139,8679]) ).

thf(8722,plain,
    ! [A: bool] :
      ( ~ ( pp @ A )
      | ( ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ A )
       != ( bot_bot @ ( fun @ bool @ bool ) ) ) ),
    inference(pattern_uni,[status(thm)],[8721:[bind(A,$thf( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ D )),bind(B,$thf( D ))]]) ).

thf(8732,plain,
    ! [A: bool] :
      ( ~ ( pp @ A )
      | ( ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ A )
       != ( bot_bot @ ( fun @ bool @ bool ) ) ) ),
    inference(simp,[status(thm)],[8722]) ).

thf(121,axiom,
    ! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_tree_Orecs_I2_J) ).

thf(503,plain,
    ! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
      = ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(641,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( D
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( B
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(642,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) @ A ) )
      | ( C
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( A )),bind(B,$thf( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(654,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) @ B )
     != ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) @ A ) ),
    inference(simp,[status(thm)],[642]) ).

thf(2178,plain,
    ! [B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ $o @ B @ $true )
     != ( huffma2021818691e_Leaf @ $o @ A @ $false ) ),
    inference(simp,[status(thm)],[2177]) ).

thf(2203,plain,
    ! [B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ $o @ B @ $true )
     != ( huffma2021818691e_Leaf @ $o @ A @ $false ) ),
    inference(simp,[status(thm)],[2178]) ).

thf(25,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
     => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_IntD1) ).

thf(205,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
     => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(645,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ D ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( B
       != ( huffma1134658180e_cost @ a @ t_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(646,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ t_1 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ C ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( A )),bind(B,$thf( huffma1134658180e_cost @ a @ t_1 )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(657,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ t_1 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ C ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[646]) ).

thf(1082,plain,
    ! [D: nat,C: huffma1450048681e_tree @ a,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ A ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C != t_2 ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1083,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_2 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ A ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1082:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 ))]]) ).

thf(1167,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_2 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ A ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1083]) ).

thf(651,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ D @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( B
       != ( huffma83463279weight @ a @ t_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(652,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma83463279weight @ a @ t_1 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ C @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[651:[bind(A,$thf( A )),bind(B,$thf( huffma83463279weight @ a @ t_1 )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(662,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma83463279weight @ a @ t_1 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ C @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[652]) ).

thf(94,axiom,
    one @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).

thf(412,plain,
    one @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(617,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ B @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
      | ( D != w ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(618,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ w @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ B @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[617:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( w ))]]) ).

thf(98,axiom,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add_Ocomm__neutral) ).

thf(425,plain,
    ! [TA: $tType] :
      ( ( comm_monoid_add @ TA )
     => ! [A: TA] :
          ( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(161,plain,
    ! [TA: $tType,C: TA,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
      | ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
    inference(cnf,[status(esa)],[158]) ).

thf(51,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
          = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_inf__assoc) ).

thf(279,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
          = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(148,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( semilattice_inf @ TA )
      | ( ( inf_inf @ TA @ A @ A )
        = A ) ),
    inference(cnf,[status(esa)],[147]) ).

thf(149,plain,
    ! [TA: $tType,A: TA] :
      ( ( ( inf_inf @ TA @ A @ A )
        = A )
      | ~ ( semilattice_inf @ TA ) ),
    inference(lifteq,[status(thm)],[148]) ).

thf(15,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Int__left__commute) ).

thf(178,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(179,plain,
    ! [TA: $tType,C: fun @ TA @ bool,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
    inference(cnf,[status(esa)],[178]) ).

thf(180,plain,
    ! [TA: $tType,C: fun @ TA @ bool,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
    inference(lifteq,[status(thm)],[179]) ).

thf(57,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_inf_Oleft__commute) ).

thf(296,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(54,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(286,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(5939,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TG @ TH ) )
      | ( ( bounded_lattice @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) )
       != ( bounded_lattice @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[5482,144]) ).

thf(5940,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( bounded_lattice_bot @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5939:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ))]]) ).

thf(1388,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
       != ( huffma2021818691e_Leaf @ $o @ A
          @ ( C
            | D ) ) )
      | ~ ( C
          | D ) ),
    inference(prim_subst,[status(thm)],[1372:[bind(A,$thf( D | E ))]]) ).

thf(1401,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ D
      | ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
       != ( huffma2021818691e_Leaf @ $o @ A
          @ ( C
            | D ) ) ) ),
    inference(cnf,[status(esa)],[1388]) ).

thf(1403,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ D
      | ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
       != ( huffma2021818691e_Leaf @ $o @ A
          @ ( C
            | D ) ) ) ),
    inference(simp,[status(thm)],[1401]) ).

thf(203,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,C: fun @ TC @ ( fun @ TB @ TA ),B: fun @ TC @ TB,A: TC] :
      ( ( aa @ TC @ TA @ ( combs @ TC @ TB @ TA @ C @ B ) @ A )
      = ( aa @ TB @ TA @ ( aa @ TC @ ( fun @ TB @ TA ) @ C @ A ) @ ( aa @ TC @ TB @ B @ A ) ) ),
    inference(cnf,[status(esa)],[202]) ).

thf(204,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,C: fun @ TC @ ( fun @ TB @ TA ),B: fun @ TC @ TB,A: TC] :
      ( ( aa @ TC @ TA @ ( combs @ TC @ TB @ TA @ C @ B ) @ A )
      = ( aa @ TB @ TA @ ( aa @ TC @ ( fun @ TB @ TA ) @ C @ A ) @ ( aa @ TC @ TB @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[203]) ).

thf(133,axiom,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
        = ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_of__nat__1) ).

thf(545,plain,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
        = ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(95,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

thf(413,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
          = ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(1056,plain,
    ! [D: nat,C: huffma1450048681e_tree @ a,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ A @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
      | ( C != t_1 ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1057,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_1 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ A @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1056:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 ))]]) ).

thf(1154,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_1 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ A @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1057]) ).

thf(190,plain,
    ! [TA: $tType,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ),
    inference(cnf,[status(esa)],[189]) ).

thf(191,plain,
    ! [TA: $tType,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ),
    inference(lifteq,[status(thm)],[190]) ).

thf(90,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma107959123e_case @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_tree_Osimps_I5_J) ).

thf(402,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
      ( ( huffma107959123e_case @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(1413,plain,
    ! [F: nat,E: nat,D: nat,C: huffma1450048681e_tree @ $o,B: nat,A: huffma1450048681e_tree @ $o] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ A ) )
      | ( A
       != ( huffma2021818691e_Leaf @ $o @ F @ $false ) )
      | ( C
       != ( huffma2021818691e_Leaf @ $o @ E @ $true ) ) ),
    inference(paramod_ordered,[status(thm)],[157,1405]) ).

thf(1414,plain,
    ! [E: nat,D: nat,C: nat,B: nat,A: huffma1450048681e_tree @ $o] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ C @ ( huffma2021818691e_Leaf @ $o @ E @ $true ) )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ A ) )
      | ( A
       != ( huffma2021818691e_Leaf @ $o @ D @ $false ) ) ),
    inference(pattern_uni,[status(thm)],[1413:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma2021818691e_Leaf @ $o @ G @ $true )),bind(D,$thf( D )),bind(E,$thf( G )),bind(F,$thf( F ))]]) ).

thf(1428,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ ( huffma2021818691e_Leaf @ $o @ D @ $true ) )
     != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ A @ ( huffma2021818691e_Leaf @ $o @ C @ $false ) ) ),
    inference(simp,[status(thm)],[1414]) ).

thf(68,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ A )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_inf__sup__aci_I1_J) ).

thf(335,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ A )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(16,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
          = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_inf__sup__aci_I2_J) ).

thf(181,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
          = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(792,plain,
    ! [TB: $tType,E: TB,D: nat,C: fun @ TB @ bool,B: nat,A: fun @ TB @ bool] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ B @ A ) )
      | ~ ( pp @ ( aa @ TB @ bool @ C @ E ) )
      | ( A
       != ( bot_bot @ ( fun @ TB @ bool ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,580]) ).

thf(793,plain,
    ! [TB: $tType,D: TB,C: nat,B: fun @ TB @ bool,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ C @ B )
       != ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ A @ ( bot_bot @ ( fun @ TB @ bool ) ) ) )
      | ~ ( pp @ ( aa @ TB @ bool @ B @ D ) ) ),
    inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( bot_bot @ ( fun @ TB @ bool ) ))]]) ).

thf(1224,plain,
    ! [TA: $tType,D: TA,C: nat,B: fun @ TA @ bool,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TA @ bool ) @ C @ B )
       != ( huffma2021818691e_Leaf @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
      | ~ ( pp @ ( aa @ TA @ bool @ B @ D ) ) ),
    inference(simp,[status(thm)],[793]) ).

thf(159,plain,
    ! [TA: $tType,C: TA,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
      | ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
      | ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[158]) ).

thf(92,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA] :
          ( ( plus_plus @ TA @ B @ A )
          = ( plus_plus @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

thf(406,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA] :
          ( ( plus_plus @ TA @ B @ A )
          = ( plus_plus @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(97,axiom,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA )
     => ! [A: TA,B: TA] :
          ( ( B
            = ( plus_plus @ TA @ B @ A ) )
        <=> ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__0__iff) ).

thf(419,plain,
    ! [TA: $tType] :
      ( ( semiri456707255roduct @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( B
              = ( plus_plus @ TA @ B @ A ) )
           => ( A
              = ( zero_zero @ TA ) ) )
          & ( ( A
              = ( zero_zero @ TA ) )
           => ( B
              = ( plus_plus @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(82,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA] :
      ( ( huffma1352802255e_freq @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) @ D )
      = ( plus_plus @ nat @ ( huffma1352802255e_freq @ TA @ B @ D ) @ ( huffma1352802255e_freq @ TA @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_freq_Osimps_I2_J) ).

thf(377,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA] :
      ( ( huffma1352802255e_freq @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) @ D )
      = ( plus_plus @ nat @ ( huffma1352802255e_freq @ TA @ B @ D ) @ ( huffma1352802255e_freq @ TA @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(33,axiom,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_inf__sup__aci_I3_J) ).

thf(230,plain,
    ! [TA: $tType] :
      ( ( lattice @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(39,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_inf__left__idem) ).

thf(245,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(123,axiom,
    cancel146912293up_add @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).

thf(509,plain,
    cancel146912293up_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(48,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(271,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(4387,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TC @ TD ) )
      | ( ( bounded_lattice @ ( fun @ TB @ ( fun @ TA @ bool ) ) )
       != ( bounded_lattice @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[3872,144]) ).

thf(4388,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( bounded_lattice_bot @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ),
    inference(pattern_uni,[status(thm)],[4387:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( fun @ TB @ ( fun @ TA @ bool ) ))]]) ).

thf(77,axiom,
    pp @ fTrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

thf(362,plain,
    pp @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(86,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( plus_plus @ TA @ A @ A ) )
        <=> ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_double__zero__sym) ).

thf(387,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( ( zero_zero @ TA )
              = ( plus_plus @ TA @ A @ A ) )
           => ( A
              = ( zero_zero @ TA ) ) )
          & ( ( A
              = ( zero_zero @ TA ) )
           => ( ( zero_zero @ TA )
              = ( plus_plus @ TA @ A @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(64,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A )
      = ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Int__assoc) ).

thf(323,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A )
      = ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1072,plain,
    ! [D: nat,C: huffma1450048681e_tree @ a,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ A ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C != t_1 ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1073,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_1 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ A ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1072:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 ))]]) ).

thf(1162,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_1 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ A ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1073]) ).

thf(126,axiom,
    comm_monoid_add @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).

thf(520,plain,
    comm_monoid_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(625,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ B ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( D
       != ( huffma83463279weight @ a @ t_2 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(626,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ ( huffma83463279weight @ a @ t_2 ) @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ B ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[625:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( huffma83463279weight @ a @ t_2 ))]]) ).

thf(127,axiom,
    zero @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

thf(521,plain,
    zero @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(89,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
      = ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_nat__add__assoc) ).

thf(399,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
      = ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(58,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
        = ( bot_bot @ ( fun @ TA @ bool ) ) )
    <=> ! [C: TA] :
          ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
         => ! [D: TA] :
              ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) )
             => ( C != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_disjoint__iff__not__equal) ).

thf(299,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
          = ( bot_bot @ ( fun @ TA @ bool ) ) )
       => ! [C: TA] :
            ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
           => ! [D: TA] :
                ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) )
               => ( C != D ) ) ) )
      & ( ! [C: TA] :
            ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
           => ! [D: TA] :
                ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) )
               => ( C != D ) ) )
       => ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
          = ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(639,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ D )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( B
       != ( huffma1134658180e_cost @ a @ t_2 ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(640,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ t_2 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ C )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( A )),bind(B,$thf( huffma1134658180e_cost @ a @ t_2 )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(653,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ t_2 ) @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ C )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[640]) ).

thf(6484,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TI @ TJ ) )
      | ( ( bounded_lattice @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[6394,144]) ).

thf(6485,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( bounded_lattice_bot @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6484:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ))]]) ).

thf(166,plain,
    ! [TA: $tType,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
      = ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[165]) ).

thf(167,plain,
    ! [TA: $tType,B: fun @ TA @ bool,A: fun @ TA @ bool] :
      ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) )
      = ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ),
    inference(lifteq,[status(thm)],[166]) ).

thf(4425,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TD @ TE ) )
      | ( ( bounded_lattice @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) )
       != ( bounded_lattice @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[4386,144]) ).

thf(4426,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( bounded_lattice_bot @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[4425:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ))]]) ).

thf(1080,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ A @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C
       != ( huffma83463279weight @ a @ t_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1081,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma83463279weight @ a @ t_1 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ A @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1080:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma83463279weight @ a @ t_1 )),bind(D,$thf( D ))]]) ).

thf(1166,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma83463279weight @ a @ t_1 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ A @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1081]) ).

thf(81,axiom,
    ! [TA: $tType,A: TA,B: TA,C: nat] :
      ( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_depth_Osimps_I1_J) ).

thf(374,plain,
    ! [TA: $tType,A: TA,B: TA,C: nat] :
      ( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(42,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
          = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_inf_Oassoc) ).

thf(255,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
          = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(486,plain,
    ! [TA: $tType,E: nat,D: huffma1450048681e_tree @ TA,C: huffma1450048681e_tree @ TA,B: nat,A: TA] :
      ( ( huffma1146269203erNode @ TA @ E @ D @ C )
     != ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
    inference(cnf,[status(esa)],[485]) ).

thf(487,plain,
    ! [TA: $tType,E: nat,D: huffma1450048681e_tree @ TA,C: huffma1450048681e_tree @ TA,B: nat,A: TA] :
      ( ( huffma1146269203erNode @ TA @ E @ D @ C )
     != ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
    inference(lifteq,[status(thm)],[486]) ).

thf(2193,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ $o @ B
          @ ( C
            | D ) )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) )
      | ~ ( C
          | D ) ),
    inference(prim_subst,[status(thm)],[2177:[bind(A,$thf( A )),bind(B,$thf( D | E ))]]) ).

thf(2200,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ C
      | ( ( huffma2021818691e_Leaf @ $o @ B
          @ ( C
            | D ) )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) ) ),
    inference(cnf,[status(esa)],[2193]) ).

thf(2202,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ C
      | ( ( huffma2021818691e_Leaf @ $o @ B
          @ ( C
            | D ) )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) ) ),
    inference(simp,[status(thm)],[2200]) ).

thf(623,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( B
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( D
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(624,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( B
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[623:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ))]]) ).

thf(663,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) @ B )
     != ( huffma2021818691e_Leaf @ TA @ ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) @ A ) ),
    inference(simp,[status(thm)],[624]) ).

thf(134,axiom,
    semiring_char_0 @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).

thf(548,plain,
    semiring_char_0 @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(5483,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TF @ TG ) )
      | ( ( bounded_lattice @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) )
       != ( bounded_lattice @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[4994,144]) ).

thf(5484,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( bounded_lattice_bot @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[5483:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ))]]) ).

thf(93,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ C @ A ) )
         => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_add__left__imp__eq) ).

thf(409,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ C @ A ) )
         => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(45,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_inf_Oleft__idem) ).

thf(263,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(52,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ TA @ bool @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_inf1D1) ).

thf(282,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ TA @ bool @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(1060,plain,
    ! [D: nat,C: huffma1450048681e_tree @ a,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ A ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
      | ( C != t_2 ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1061,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_2 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ A ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1060:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 ))]]) ).

thf(1156,plain,
    ! [C: nat,B: nat,A: huffma1450048681e_tree @ a] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ C @ t_2 )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ a ) @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ A ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1061]) ).

thf(1421,plain,
    ! [F: nat,E: nat,D: nat,C: huffma1450048681e_tree @ $o,B: nat,A: huffma1450048681e_tree @ $o] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ A ) )
      | ( C
       != ( huffma2021818691e_Leaf @ $o @ F @ $false ) )
      | ( A
       != ( huffma2021818691e_Leaf @ $o @ E @ $true ) ) ),
    inference(paramod_ordered,[status(thm)],[157,1405]) ).

thf(1422,plain,
    ! [E: nat,D: nat,C: nat,B: huffma1450048681e_tree @ $o,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ C @ B )
       != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ A @ ( huffma2021818691e_Leaf @ $o @ E @ $true ) ) )
      | ( B
       != ( huffma2021818691e_Leaf @ $o @ D @ $false ) ) ),
    inference(pattern_uni,[status(thm)],[1421:[bind(A,$thf( huffma2021818691e_Leaf @ $o @ G @ $true )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G )),bind(F,$thf( F ))]]) ).

thf(1432,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ B @ ( huffma2021818691e_Leaf @ $o @ C @ $false ) )
     != ( huffma2021818691e_Leaf @ ( huffma1450048681e_tree @ $o ) @ A @ ( huffma2021818691e_Leaf @ $o @ D @ $true ) ) ),
    inference(simp,[status(thm)],[1422]) ).

thf(14,axiom,
    semilattice_inf @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).

thf(177,plain,
    semilattice_inf @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(108,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus @ nat @ C @ B )
        = ( plus_plus @ nat @ C @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nat__add__left__cancel) ).

thf(463,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( plus_plus @ nat @ C @ B )
          = ( plus_plus @ nat @ C @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( plus_plus @ nat @ C @ B )
          = ( plus_plus @ nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(69,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( fun @ TA @ bool ) )
      = ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_empty__def) ).

thf(338,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( fun @ TA @ bool ) )
      = ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(109,axiom,
    ! [A: a] :
      ( ( ( inf_inf @ ( fun @ a @ bool ) @ ( huffma675207370phabet @ a @ t_1 ) @ ( huffma675207370phabet @ a @ t_2 ) )
        = ( bot_bot @ ( fun @ a @ bool ) ) )
     => ( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_2 ) ) )
       => ( ( huffma410068972_depth @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) @ A )
          = ( plus_plus @ nat @ ( huffma410068972_depth @ a @ t_2 @ A ) @ ( one_one @ nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_d_092_060_094isub_0622) ).

thf(470,plain,
    ! [A: a] :
      ( ( ( inf_inf @ ( fun @ a @ bool ) @ ( huffma675207370phabet @ a @ t_1 ) @ ( huffma675207370phabet @ a @ t_2 ) )
        = ( bot_bot @ ( fun @ a @ bool ) ) )
     => ( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_2 ) ) )
       => ( ( huffma410068972_depth @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) @ A )
          = ( plus_plus @ nat @ ( huffma410068972_depth @ a @ t_2 @ A ) @ ( one_one @ nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(76,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ! [A: TB] :
          ( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
          = ( bot_bot @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bot__apply) ).

thf(359,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ! [A: TB] :
          ( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
          = ( bot_bot @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(784,plain,
    ! [TB: $tType,E: TB,D: nat,C: bool,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ D @ C )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ A )
      | ( C
       != ( aa @ TB @ bool @ ( bot_bot @ ( fun @ TB @ bool ) ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[157,580]) ).

thf(785,plain,
    ! [TB: $tType,D: TB,C: nat,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ ( aa @ TB @ bool @ ( bot_bot @ ( fun @ TB @ bool ) ) @ D ) )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ A ) ),
    inference(pattern_uni,[status(thm)],[784:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( aa @ TB @ bool @ ( bot_bot @ ( fun @ TB @ bool ) ) @ G )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).

thf(1220,plain,
    ! [TA: $tType,D: TA,C: nat,B: nat,A: bool] :
      ( ( ( huffma2021818691e_Leaf @ bool @ C @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ D ) )
       != ( huffma2021818691e_Leaf @ bool @ B @ A ) )
      | ~ ( pp @ A ) ),
    inference(simp,[status(thm)],[785]) ).

thf(543,plain,
    ! [TA: $tType,E: nat,D: TA,C: nat,B: huffma1450048681e_tree @ TA,A: huffma1450048681e_tree @ TA] :
      ( ( huffma2021818691e_Leaf @ TA @ E @ D )
     != ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
    inference(cnf,[status(esa)],[542]) ).

thf(544,plain,
    ! [TA: $tType,E: nat,D: TA,C: nat,B: huffma1450048681e_tree @ TA,A: huffma1450048681e_tree @ TA] :
      ( ( huffma2021818691e_Leaf @ TA @ E @ D )
     != ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
    inference(lifteq,[status(thm)],[543]) ).

thf(198,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
      = ( bot_bot @ ( fun @ TA @ bool ) ) ),
    inference(cnf,[status(esa)],[197]) ).

thf(199,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
      = ( bot_bot @ ( fun @ TA @ bool ) ) ),
    inference(lifteq,[status(thm)],[198]) ).

thf(67,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ( B
        = ( bot_bot @ ( fun @ TA @ bool ) ) )
     => ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_equals0D) ).

thf(331,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ( B
        = ( bot_bot @ ( fun @ TA @ bool ) ) )
     => ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(786,plain,
    ! [TB: $tType,E: TB,D: nat,C: fun @ TB @ bool,B: nat,A: fun @ TB @ bool] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ D @ C )
       != ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ B @ A ) )
      | ~ ( pp @ ( aa @ TB @ bool @ A @ E ) )
      | ( C
       != ( bot_bot @ ( fun @ TB @ bool ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,580]) ).

thf(787,plain,
    ! [TB: $tType,D: TB,C: nat,B: nat,A: fun @ TB @ bool] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ C @ ( bot_bot @ ( fun @ TB @ bool ) ) )
       != ( huffma2021818691e_Leaf @ ( fun @ TB @ bool ) @ B @ A ) )
      | ~ ( pp @ ( aa @ TB @ bool @ A @ D ) ) ),
    inference(pattern_uni,[status(thm)],[786:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( bot_bot @ ( fun @ TB @ bool ) ))]]) ).

thf(1221,plain,
    ! [TA: $tType,D: TA,C: nat,B: nat,A: fun @ TA @ bool] :
      ( ( ( huffma2021818691e_Leaf @ ( fun @ TA @ bool ) @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) )
       != ( huffma2021818691e_Leaf @ ( fun @ TA @ bool ) @ B @ A ) )
      | ~ ( pp @ ( aa @ TA @ bool @ A @ D ) ) ),
    inference(simp,[status(thm)],[787]) ).

thf(61,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ! [A: TB] :
          ( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
          = ( bot_bot @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bot__fun__def) ).

thf(314,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ! [A: TB] :
          ( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
          = ( bot_bot @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(1402,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ C
      | ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
       != ( huffma2021818691e_Leaf @ $o @ A
          @ ( C
            | D ) ) ) ),
    inference(cnf,[status(esa)],[1388]) ).

thf(1404,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ C
      | ( ( huffma2021818691e_Leaf @ $o @ B @ $false )
       != ( huffma2021818691e_Leaf @ $o @ A
          @ ( C
            | D ) ) ) ),
    inference(simp,[status(thm)],[1402]) ).

thf(104,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
      ( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
        = ( huffma1146269203erNode @ TA @ C @ B @ A ) )
    <=> ( ( F = C )
        & ( E = B )
        & ( D = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tree_Osimps_I2_J) ).

thf(446,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
      ( ( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
          = ( huffma1146269203erNode @ TA @ C @ B @ A ) )
       => ( ( F = C )
          & ( E = B )
          & ( D = A ) ) )
      & ( ( ( F = C )
          & ( E = B )
          & ( D = A ) )
       => ( ( huffma1146269203erNode @ TA @ F @ E @ D )
          = ( huffma1146269203erNode @ TA @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(78,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TA )
     => ( semilattice_inf @ ( fun @ TB @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).

thf(363,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( lattice @ TA )
     => ( semilattice_inf @ ( fun @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(131,axiom,
    ! [TA: $tType,A: TA,B: nat] :
      ( ( huffma83463279weight @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_weight_Osimps_I1_J) ).

thf(539,plain,
    ! [TA: $tType,A: TA,B: nat] :
      ( ( huffma83463279weight @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(113,axiom,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ! [A: nat,B: nat] :
          ( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ B @ A ) )
          = ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__nat__add) ).

thf(482,plain,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ! [A: nat,B: nat] :
          ( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ B @ A ) )
          = ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(1062,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( A
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
      | ( C
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1063,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( A
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1062:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) )),bind(D,$thf( D ))]]) ).

thf(1157,plain,
    ! [B: nat,A: nat] :
      ( ( huffma2021818691e_Leaf @ nat @ B @ ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
     != ( huffma2021818691e_Leaf @ nat @ A @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1063]) ).

thf(3873,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TB @ TC ) )
      | ( ( bounded_lattice @ ( fun @ TA @ bool ) )
       != ( bounded_lattice @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[3840,144]) ).

thf(3874,plain,
    ! [TA: $tType,TB: $tType] : ( bounded_lattice_bot @ ( fun @ TB @ ( fun @ TA @ bool ) ) ),
    inference(pattern_uni,[status(thm)],[3873:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( fun @ TA @ bool ))]]) ).

thf(80,axiom,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( plus_plus @ TA @ C @ B )
            = ( plus_plus @ TA @ C @ A ) )
        <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_add__left__cancel) ).

thf(368,plain,
    ! [TA: $tType] :
      ( ( cancel_semigroup_add @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ( plus_plus @ TA @ C @ B )
              = ( plus_plus @ TA @ C @ A ) )
           => ( B = A ) )
          & ( ( B = A )
           => ( ( plus_plus @ TA @ C @ B )
              = ( plus_plus @ TA @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(43,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_inf__left__commute) ).

thf(258,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) )
          = ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(18,axiom,
    ! [TA: $tType,A: TA] :
      ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
    <=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_bot__empty__eq) ).

thf(186,plain,
    ! [TA: $tType,A: TA] :
      ( ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
       => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
      & ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
       => ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(8605,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TM @ TN ) )
      | ( ( bounded_lattice @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[8024,144]) ).

thf(8606,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( bounded_lattice_bot @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8605:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(631,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ B @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( D
       != ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(632,plain,
    ! [TA: $tType,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ B @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ))]]) ).

thf(73,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
     => ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
       => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_IntI) ).

thf(351,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
     => ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
       => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(35,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
      = ( bot_bot @ ( fun @ TA @ bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Int__empty__left) ).

thf(235,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
      = ( bot_bot @ ( fun @ TA @ bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(124,axiom,
    ! [A: nat,B: nat] :
      ( ( ( plus_plus @ nat @ B @ A )
        = ( zero_zero @ nat ) )
    <=> ( ( B
          = ( zero_zero @ nat ) )
        & ( A
          = ( zero_zero @ nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__is__0) ).

thf(510,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( plus_plus @ nat @ B @ A )
          = ( zero_zero @ nat ) )
       => ( ( B
            = ( zero_zero @ nat ) )
          & ( A
            = ( zero_zero @ nat ) ) ) )
      & ( ( ( B
            = ( zero_zero @ nat ) )
          & ( A
            = ( zero_zero @ nat ) ) )
       => ( ( plus_plus @ nat @ B @ A )
          = ( zero_zero @ nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(26,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa @ TA @ TB @ B @ C )
          = ( aa @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).

thf(207,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa @ TA @ TB @ B @ C )
          = ( aa @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(1070,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ A ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C
       != ( huffma1134658180e_cost @ a @ t_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1071,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma1134658180e_cost @ a @ t_1 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ A ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1070:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( huffma1134658180e_cost @ a @ t_1 )),bind(D,$thf( D ))]]) ).

thf(1161,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( huffma1134658180e_cost @ a @ t_1 ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ A ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1071]) ).

thf(101,axiom,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: TA] :
      ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
       => ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
          = ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ C @ D ) @ ( one_one @ nat ) ) ) )
      & ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
       => ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
           => ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
              = ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ A @ D ) @ ( one_one @ nat ) ) ) )
          & ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
           => ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
              = ( zero_zero @ nat ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_depth_Osimps_I2_J) ).

thf(432,plain,
    ! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: TA] :
      ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
       => ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
          = ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ C @ D ) @ ( one_one @ nat ) ) ) )
      & ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
       => ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
           => ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
              = ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ A @ D ) @ ( one_one @ nat ) ) ) )
          & ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
           => ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
              = ( zero_zero @ nat ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(12,axiom,
    ! [TA: $tType] :
      ( ( one @ TA )
     => ! [A: TA] :
          ( ( ( one_one @ TA )
            = A )
        <=> ( A
            = ( one_one @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_one__reorient) ).

thf(168,plain,
    ! [TA: $tType] :
      ( ( one @ TA )
     => ! [A: TA] :
          ( ( ( ( one_one @ TA )
              = A )
           => ( A
              = ( one_one @ TA ) ) )
          & ( ( A
              = ( one_one @ TA ) )
           => ( ( one_one @ TA )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6924,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( bounded_lattice_bot @ ( fun @ TJ @ TK ) )
      | ( ( bounded_lattice @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[6483,144]) ).

thf(6925,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( bounded_lattice_bot @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6924:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ))]]) ).

thf(91,axiom,
    comm_semiring_1 @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).

thf(405,plain,
    comm_semiring_1 @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(182,plain,
    ! [TA: $tType,C: TA,B: TA,A: TA] :
      ( ~ ( lattice @ TA )
      | ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
        = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[181]) ).

thf(183,plain,
    ! [TA: $tType,C: TA,B: TA,A: TA] :
      ( ( ( inf_inf @ TA @ ( inf_inf @ TA @ C @ B ) @ A )
        = ( inf_inf @ TA @ C @ ( inf_inf @ TA @ B @ A ) ) )
      | ~ ( lattice @ TA ) ),
    inference(lifteq,[status(thm)],[182]) ).

thf(49,axiom,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ A )
          = ( inf_inf @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_inf__commute) ).

thf(273,plain,
    ! [TA: $tType] :
      ( ( semilattice_inf @ TA )
     => ! [A: TA,B: TA] :
          ( ( inf_inf @ TA @ B @ A )
          = ( inf_inf @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(65,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
     => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_IntD2) ).

thf(326,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
     => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(70,axiom,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA )
     => ! [A: nat,B: nat] :
          ( ( ( semiring_1_of_nat @ TA @ B )
            = ( semiring_1_of_nat @ TA @ A ) )
        <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_of__nat__eq__iff) ).

thf(341,plain,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA )
     => ! [A: nat,B: nat] :
          ( ( ( ( semiring_1_of_nat @ TA @ B )
              = ( semiring_1_of_nat @ TA @ A ) )
           => ( B = A ) )
          & ( ( B = A )
           => ( ( semiring_1_of_nat @ TA @ B )
              = ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(110,axiom,
    semiri456707255roduct @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(474,plain,
    semiri456707255roduct @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(635,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ D @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) )
      | ( B != w ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(636,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ w @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ C @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[635:[bind(A,$thf( A )),bind(B,$thf( w ))]]) ).

thf(664,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ w @ A ) )
      | ( ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ C @ t_1 @ t_2 ) )
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[636]) ).

thf(130,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus @ nat @ C @ B )
        = ( plus_plus @ nat @ A @ B ) )
    <=> ( C = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nat__add__right__cancel) ).

thf(532,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( plus_plus @ nat @ C @ B )
          = ( plus_plus @ nat @ A @ B ) )
       => ( C = A ) )
      & ( ( C = A )
       => ( ( plus_plus @ nat @ C @ B )
          = ( plus_plus @ nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(1078,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ D @ C )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ A @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( C
       != ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,136]) ).

thf(1079,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ A @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1078:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) )),bind(D,$thf( D ))]]) ).

thf(1165,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( huffma2021818691e_Leaf @ nat @ C @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) )
       != ( huffma2021818691e_Leaf @ nat @ B @ A ) )
      | ( ( plus_plus @ nat @ ( plus_plus @ nat @ A @ ( huffma83463279weight @ a @ t_2 ) ) @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[1079]) ).

thf(37,axiom,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
          = ( bot_bot @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_inf__bot__right) ).

thf(239,plain,
    ! [TA: $tType] :
      ( ( bounded_lattice_bot @ TA )
     => ! [A: TA] :
          ( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
          = ( bot_bot @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(38,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

thf(242,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(56,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ( bot @ ( fun @ TB @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).

thf(294,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ( bot @ ( fun @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(2199,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ D
      | ( ( huffma2021818691e_Leaf @ $o @ B
          @ ( C
            | D ) )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) ) ),
    inference(cnf,[status(esa)],[2193]) ).

thf(2201,plain,
    ! [D: $o,C: $o,B: nat,A: nat] :
      ( ~ D
      | ( ( huffma2021818691e_Leaf @ $o @ B
          @ ( C
            | D ) )
       != ( huffma2021818691e_Leaf @ $o @ A @ $false ) ) ),
    inference(simp,[status(thm)],[2199]) ).

thf(122,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
      = ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_nat__add__left__commute) ).

thf(506,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
      = ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(47,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
      = ( inf_inf @ ( fun @ TA @ bool ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Int__commute) ).

thf(268,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
      ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
      = ( inf_inf @ ( fun @ TA @ bool ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(118,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
          = ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

thf(496,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_1 @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
          = ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(41,axiom,
    bot @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).

thf(254,plain,
    bot @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(59,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).

thf(309,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(647,plain,
    ! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
       != ( huffma2021818691e_Leaf @ TA @ B @ A ) )
      | ( ( plus_plus @ nat @ D @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) )
      | ( B
       != ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[156,136]) ).

thf(648,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ A ) )
      | ( ( plus_plus @ nat @ C @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[647:[bind(A,$thf( A )),bind(B,$thf( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(659,plain,
    ! [TA: $tType,C: nat,B: TA,A: TA] :
      ( ( ( huffma2021818691e_Leaf @ TA @ C @ B )
       != ( huffma2021818691e_Leaf @ TA @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ a @ t_1 ) @ ( huffma1134658180e_cost @ a @ t_1 ) ) @ ( huffma83463279weight @ a @ t_2 ) ) @ A ) )
      | ( ( plus_plus @ nat @ C @ ( huffma1134658180e_cost @ a @ t_2 ) )
       != ( huffma1134658180e_cost @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ) ) ) ),
    inference(simp,[status(thm)],[648]) ).

thf(8740,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( bounded_lattice @ ( fun @ TN @ TO ) )
      | ( ( bounded_lattice @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( bounded_lattice @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[8604,176]) ).

thf(8741,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( bounded_lattice @ ( fun @ TN @ ( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[8740:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( fun @ TM @ ( fun @ TL @ ( fun @ TK @ ( fun @ TJ @ ( fun @ TI @ ( fun @ TH @ ( fun @ TG @ ( fun @ TF @ ( fun @ TE @ ( fun @ TD @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(116,axiom,
    ( ( bot_bot @ nat )
    = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_bot__nat__def) ).

thf(491,plain,
    ( ( bot_bot @ nat )
    = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(10630,plain,
    $false,
    inference(e,[status(thm)],[1168,347,628,3397,3863,481,365,9273,1369,1406,655,1158,582,217,276,202,597,1426,384,8635,142,8622,500,1164,185,5938,320,6483,4386,1430,184,4415,3495,1330,196,157,542,460,559,3840,189,6396,606,284,416,6923,228,2158,289,261,475,164,211,485,238,353,7492,1714,147,2979,4996,396,660,1345,1405,428,312,2861,634,233,248,380,439,2204,529,1438,1153,381,220,2296,3852,201,1730,1163,1223,160,5956,561,429,165,192,3884,630,2150,137,197,8026,4994,2872,522,1159,493,456,3408,519,317,156,1328,8604,3386,356,610,499,328,1160,488,1361,4983,193,669,8743,2312,1155,9260,622,393,8013,2304,2243,457,8732,569,503,4970,654,2203,266,205,2883,657,1167,586,662,412,618,6053,425,161,279,3375,573,2894,149,601,180,296,176,286,5940,1403,204,545,413,584,1154,191,402,1428,445,5471,144,335,2166,181,1224,350,159,8042,406,419,377,230,1722,245,509,271,599,4388,362,567,387,5584,323,140,1162,520,626,3971,521,399,7479,6394,5482,2288,299,267,653,223,608,135,563,6485,167,4426,675,7490,1166,162,374,255,487,2202,663,548,194,145,7600,580,5927,150,5484,3872,409,263,282,1156,1432,177,463,338,470,359,1220,544,199,673,331,6912,1738,8024,7466,6899,1221,1353,175,314,143,8679,1404,446,571,1372,595,4424,6425,363,539,482,671,1157,3874,1189,368,2174,258,186,8606,632,139,158,351,235,510,1777,207,667,6412,4404,1161,432,168,146,6925,405,183,273,210,326,341,474,664,532,1165,239,242,294,2201,136,506,268,8093,200,8147,178,5458,496,2177,254,227,309,659,8741,2351,491]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWW535_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.13  % Command  : run_Leo-III %s %d THM
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jun 19 08:43:10 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.98/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.63/1.09  % [INFO] 	 Parsing done (210ms). 
% 1.63/1.10  % [INFO] 	 Running in sequential loop mode. 
% 2.25/1.33  % [INFO] 	 eprover registered as external prover. 
% 2.25/1.33  % [INFO] 	 Scanning for conjecture ... 
% 2.79/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 132 axioms. Running axiom selection ... 
% 3.03/1.53  % [INFO] 	 Axiom selection finished. Selected 132 axioms (removed 0 axioms). 
% 3.59/1.68  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.69/1.70  % [INFO] 	 Type checking passed. 
% 3.69/1.70  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 4.13/1.87  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 4.13/1.87  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 120.71/43.04  % External prover 'e' found a proof!
% 120.71/43.04  % [INFO] 	 Killing All external provers ... 
% 120.71/43.04  % Time passed: 42494ms (effective reasoning time: 41934ms)
% 120.71/43.04  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 120.71/43.04  % Axioms used in derivation (132): arity_Nat_Onat___Orderings_Obot, fact_10_tree_Orecs_I2_J, fact_3_cost_Osimps_I2_J, fact_86_bot__fun__def, help_COMBS_1_1_U, fact_71_Int__left__commute, fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_29_weight_Osimps_I1_J, fact_36_one__reorient, fact_47_emptyE, help_fconj_3_1_U, fact_44_empty__Collect__eq, fact_63_inf__left__commute, arity_Nat_Onat___Rings_Osemiring__1, arity_fun___Orderings_Obot, fact_82_disjoint__iff__not__equal, fact_2_weight_Osimps_I2_J, fact_65_inf__sup__aci_I2_J, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_64_inf_Oassoc, fact_81_Int__empty__right, fact_30_tree_Osimps_I4_J, fact_58_inf__sup__aci_I1_J, fact_75_mem__def, fact_84_inf__apply, fact_34_of__nat__1, fact_32_of__nat__eq__iff, fact_26_tree_Orecs_I1_J, fact_42_inf1I, arity_fun___Lattices_Olattice, fact_39_inf1E, fact_69_Int__commute, arity_HOL_Obool___Lattices_Obounded__lattice__bot, fact_96_add__0__iff, fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_78_inf1D1, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_70_Int__left__absorb, fact_80_Int__empty__left, fact_50_Int__iff, fact_87_bot__apply, help_fFalse_1_1_T, fact_66_inf__assoc, fact_9_tree_Osimps_I6_J, fact_74_ext, help_COMBB_1_1_U, fact_16_add__right__imp__eq, fact_8_freq_Osimps_I2_J, arity_HOL_Obool___Lattices_Osemilattice__inf, fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_1_InnerNode_Oprems, fact_37_inf__bot__right, fact_13_nat__add__assoc, fact_59_inf__commute, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_76_Collect__def, help_fconj_2_1_U, fact_77_IntD2, fact_57_inf_Ocommute, fact_89_double__zero__sym, arity_Nat_Onat___Lattices_Olattice, fact_17_add__imp__eq, arity_fun___Lattices_Osemilattice__inf, fact_90_add__is__0, fact_33_tree_Osimps_I1_J, fact_38_inf__bot__left, fact_60_inf__sup__aci_I4_J, fact_52_empty__def, fact_6_add__left__cancel, fact_72_Int__assoc, fact_73_IntD1, fact_27_d_092_060_094isub_0622, fact_79_inf1D2, fact_67_Int__absorb, arity_Nat_Onat___Rings_Ocomm__semiring__1, arity_Nat_Onat___Groups_Ozero, arity_Nat_Onat___Lattices_Osemilattice__inf, fact_12_nat__add__left__commute, arity_HOL_Obool___Lattices_Obounded__lattice, fact_95_bot__nat__def, help_COMBK_1_1_U, fact_55_inf_Oidem, fact_88_exists__in__alphabet, fact_93_freq_Osimps_I1_J, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, fact_85_depth_Osimps_I2_J, fact_21_ab__semigroup__add__class_Oadd__ac_I1_J, fact_54_equals0D, arity_Nat_Onat___Nat_Osemiring__char__0, help_fconj_1_1_U, fact_56_inf__idem, fact_43_all__not__in__conv, fact_92_depth_Osimps_I1_J, fact_11_nat__add__commute, arity_Nat_Onat___Groups_Oone, fact_5_nat__add__right__cancel, help_fFalse_1_1_U, fact_68_Int__def, fact_45_empty__iff, fact_62_inf__sup__aci_I3_J, arity_HOL_Obool___Lattices_Olattice, fact_61_inf_Oleft__commute, fact_7_add__right__cancel, fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_0_tree_Osimps_I2_J, fact_48_inf_Oleft__idem, help_pp_1_1_U, fact_51_bot__empty__eq, fact_25_consistent_Osimps_I1_J, arity_fun___Lattices_Obounded__lattice__bot, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_94_cost_Osimps_I1_J, fact_91_of__nat__0, fact_40_IntE, fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_53_ex__in__conv, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_28_of__nat__add, help_pp_2_1_U, fact_4_nat__add__left__cancel, arity_fun___Lattices_Obounded__lattice, fact_46_Collect__empty__eq, fact_18_add__left__imp__eq, fact_97_add_Ocomm__neutral, fact_31_tree_Osimps_I3_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_41_IntI, fact_35_consistent_Osimps_I2_J, fact_49_inf__left__idem, fact_24_tree_Osimps_I5_J, fact_83_inf__fun__def
% 120.71/43.04  % No. of inferences in proof: 686
% 120.71/43.04  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 42494 ms resp. 41934 ms w/o parsing
% 121.56/43.28  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 121.56/43.29  % [INFO] 	 Killing All external provers ... 
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